CFA Level I Exam · Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Valuing Forward Contracts During Their Life: Long and Short Positions

Updated 7 October 2026 · Fact-checked

A forward contract's value at time t is the present value of the difference between the current forward price and the original contract price. For a long, Vt = PV of [F(t) − F(0)]. A short is the negative of that. At initiation the value is zero. At expiration it is ST − F(0) for a long.

Understand Valuing Forward Contracts During Their Life

A forward contract costs nothing to enter. The forward price is set so that both sides see zero value on day one. That is why no cash changes hands at initiation (apart from any collateral).

After that, the market moves. The spot price changes, interest rates change, and so the forward price for the same delivery date changes. Your contract still locks in the old price, F(0). A new contract would lock in the new price, F(t). The value of your contract is the gap between the two.

That gap is paid at expiration, not today. So you discount it back to today at the rate for the remaining time. This is why the formula is a present value of a price difference.

The long gains when the forward price rises: they locked in a cheaper purchase price. The short loses. A forward is a zero-sum contract, so the short's value is exactly the negative of the long's value.

At expiration there is no time left, so no discounting. The long's value is the spot price at expiry minus the agreed price. The forward price at expiry equals the spot price, because delivery is immediate.

Key formulas to remember

Value at initiation: V0(long) = V0(short) = 0; The forward price F(0) is set to make the contract worth zero to both parties.
Value of a long forward at time t (using forward prices): Vt(long) = [F(t) − F(0)] ÷ (1 + r)^(T − t); F(t) is the new forward price for the same expiry T. r is the annual rate for the remaining time T − t. Use continuous compounding as e^(−r(T − t)) if the question says so.
Value of a short forward at time t: Vt(short) = −Vt(long) = [F(0) − F(t)] ÷ (1 + r)^(T − t); Same size as the long, opposite sign.
Value at expiration: VT(long) = ST − F(0); VT(short) = F(0) − ST; No discounting, because T − t = 0 and F(T) = ST.
Value of a long forward on an asset with no cash flows: Vt(long) = St − F(0) ÷ (1 + r)^(T − t); Equivalent to the first formula when F(t) = St × (1 + r)^(T − t). Use it when the question gives the spot price.
Value with benefits or costs of holding the asset: Vt(long) = [St − PVt(benefits) + PVt(costs)] − F(0) ÷ (1 + r)^(T − t); Adjust the spot price for the present value of income (subtract) and storage costs (add) over the remaining life.

How to solve Valuing Forward Contracts During Their Life questions

Use this method for any question that asks for the value of an existing forward, for either party, at any date.

1Identify the position: long (buyer) or short (seller). Note the original forward price F(0) and the expiry date T.
2Find the time left, T − t, in years. For example, 3 months left is 0.25.
3Find the current forward price F(t) for the same expiry. If it is not given, compute it from spot: F(t) = St × (1 + r)^(T − t), adjusted for any income or costs.
4Compute the price difference F(t) − F(0) for the long.
5Discount that difference at the rate for the remaining time, (1 + r)^(T − t).
6Flip the sign if you are asked for the short.
7Sanity check: if the forward price rose, the long should be positive and the short negative.

Quickest way: Spot-minus-discounted-price shortcut

When to use it: Use when the question gives the spot price, the original forward price, the rate and the time left, and the asset pays no income.

Compute the discounted original price: F(0) ÷ (1 + r)^(T − t).
Subtract it from spot: Vt(long) = St − that number.
On the BA II Plus: enter 1 + r (for example 1.04), press yx, enter the time left (for example 0.75), press =. This gives (1 + r)^(T − t). Then divide F(0) by that result: press STO 1, then enter 105 ÷ RCL 1 =.
On the HP 12C: enter F(0) and press ENTER (105 ENTER), then enter 1 + r and press ENTER (1.04 ENTER), then enter the time left and press yx (0.75 yx), then press ÷. The display shows F(0) ÷ (1 + r)^(T − t).
Change sign for the short. Eliminate any option whose sign contradicts the direction of price movement.

Common mistakes in Valuing Forward Contracts During Their Life

Forgetting to discount the price difference.
The difference F(t) − F(0) looks like the answer, and students stop there.
Fix: The gain is received at T. Always divide by (1 + r)^(T − t) when time remains.
Using the original time to expiry instead of the time remaining.
The question gives a 1-year contract, so students reuse 1 year.
Fix: Use T − t. If 3 months have passed on a 1-year contract, discount for 0.75 years.
Giving the short the same sign as the long.
Students compute once and report it for both parties.
Fix: A forward is zero-sum. The short's value is the negative of the long's.
Using the spot price as the forward price F(t).
Spot and forward prices look similar.
Fix: F(t) = St × (1 + r)^(T − t) for no-income assets. Or use the spot formula, St − F(0) ÷ (1 + r)^(T − t), which handles this directly.
Ignoring income or storage costs on the underlying.
Students memorise the no-cash-flow formula only.
Fix: Subtract the present value of dividends or coupons from spot, and add the present value of storage costs, before applying the formula.
Discounting the expiration value.
Students apply one formula to every date.
Fix: At expiration T − t = 0. Value is just ST − F(0) for the long.

Worked examples

Example 1

A trader entered a long forward on a non-dividend-paying stock 3 months ago, with a 1-year expiry and a forward price of $105. Spot is now $108 and the annual rate is 4%. What is the value of the long position to the nearest cent? (Options: A. $3.00, B. $6.04, C. $6.11)

Show the solution

Time left: 1 year − 3 months = 0.75 years.
Discount factor: 1.04^0.75. ln(1.04) = 0.039221; × 0.75 = 0.029416; e^0.029416 = 1.02985.
Discounted original price: 105 ÷ 1.02985 = 101.96.
Value of long = 108 − 101.96 = 6.04.
Sanity check: spot is above the discounted original price, so the long is positive. Option B matches.

Answer: B. The long position is worth about $6.04.

Example 2

A short forward on a non-dividend-paying stock was agreed at a forward price of $50. With 6 months left, spot is $46 and the annual rate is 6%. What is the value of the short position, to the nearest cent?

Show the solution

Time left: 0.5 years.
Discount factor: 1.06^0.5 = √1.06 = 1.029563.
Discounted original price: 50 ÷ 1.029563 = 48.5642.
Value of long = 46 − 48.5642 = −2.5642.
Short is the negative of the long: +2.5642.
Sanity check: spot has fallen, so the forward price has fallen, and the short gains. A positive value fits.

Answer: The short is worth about $2.56.

Exam tips

Look at the direction first. The long is positive if the current forward price F(t) is above F(0), or equivalently if St is above F(0) ÷ (1 + r)^(T − t). The long is negative if it is below. Do not assume any rise in spot makes the long positive, because the discounted original price also grows toward F(0) over time. Checking the sign this way helps you eliminate options with the wrong sign.
Read whether the question gives F(t) or only spot. If spot, use St − F(0) ÷ (1 + r)^(T − t).
Check which party the question asks about. Examiners often ask for the short to test sign handling.
Watch the time units. Months must become years before discounting.
At expiration, ignore rates entirely and use ST − F(0).

Practice questions from Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Valuing Forward Contracts During Their Life in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Valuing Forward Contracts During Their Life: frequently asked questions

What is the value of a forward contract at initiation?

It is zero for both the long and the short. The forward price is set so that neither side pays to enter. Any collateral posted is separate from the contract's value.

How do I value a forward contract at expiration?

For the long, value is the spot price at expiration minus the original forward price. For the short, it is the original forward price minus spot. There is no discounting at expiration.

Why do we discount the difference between forward prices?

The difference between the new and old forward price is settled at expiration, not today. Its value today is the present value at the rate for the remaining time.

How does the value change if the underlying pays dividends?

Reduce the spot price by the present value of dividends expected over the remaining life, then apply the usual formula. Storage costs are added instead.